椭圆曲线数据：

cjsh

Elliptic Curve Data
http://www.warwick.ac.uk/staff/J.E.Cremona//ftp/data/

可在Cremona站或SAGE文档中找到求RANK的唯一方法
[br][br]-=-=-=-=- 以下内容由 cjsh 在 时添加 -=-=-=-=-
cremona，Stein-Watkins 的有理域，John Jones数域多项式
http://www.warwick.ac.uk/staff/J.E.Cremona/book/fulltext/index.html
前导子N分类的，默认前10000，可加载大的到130000
from sage.databases.cremona import LargeCremonaDatabase

随机选一条：
CremonaDatabase().random()
Elliptic Curve defined by y^2 + x*y = x^3 - x^2 + 324*x - 18068 over
Rational FieldElliptic Curve defined by y^2 + x*y = x^3 - x^2 + 324*x - 18068 over Rational Field
新老版cremona字母转换：
old_cremona_letter_code(5221)
';UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU\
UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU\
UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU';

标签分离：
c = CremonaDatabase()
parse_cremona_label(';37a2';)

import sage.databases.cremona as cremona
cremona.split_code(';37a2';)

求前导子21的所有曲线：
c = CremonaDatabase()
c.allcurves(21)

{';a1';: [[1, 0, 0, -4, -1], 0, 8], ';a3';: [[1, 0, 0, -39, 90], 0, 8],
';a2';: [[1, 0, 0, -49, -136], 0, 4], ';a5';: [[1, 0, 0, -784, -8515], 0,
2], ';a4';: [[1, 0, 0, 1, 0], 0, 4], ';a6';: [[1, 0, 0, -34, -217], 0, 2]}{';a1';: [[1, 0, 0, -4, -1], 0, 8], ';a3';: [[1, 0, 0, -39, 90], 0, 8], ';a2';: [[1, 0, 0, -49, -136], 0, 4], ';a5';: [[1, 0, 0, -784, -8515], 0, 2], ';a4';: [[1, 0, 0, 1, 0], 0, 4], ';a6';: [[1, 0, 0, -34, -217], 0, 2]}
从5个不变量定义曲线:要CremonaData理的才行：
c = CremonaDatabase()
sage: c.elliptic_curve_from_ainvs(11, [0, -1, 1, -10, -20])
列出给定前导子的所有曲线：
c = CremonaDatabase()
CremonaDatabase().list([3171])
[Elliptic Curve defined by y^2 + y = x^3 - x^2 - 7*x - 9 over Rational
Field, Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 49*x - 58
over Rational Field, Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2
- 454*x + 3506 over Rational Field, Elliptic Curve defined by y^2 + x*y
+ y = x^3 + x^2 - 7249*x + 234536 over Rational Field, Elliptic Curve
defined by y^2 + x*y + y = x^3 + x^2 - 139*x + 8672 over Rational Field,
Elliptic Curve defined by y^2 + y = x^3 + x^2 - 14*x + 3677 over
Rational Field][Elliptic Curve defined by y^2 + y = x^3 - x^2 - 7*x - 9 over Rational Field, Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 49*x - 58 over Rational Field, Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 454*x + 3506 over Rational Field, Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 7249*x + 234536 over Rational Field, Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 139*x + 8672 over Rational Field, Elliptic Curve defined by y^2 + y = x^3 + x^2 - 14*x + 3677 over Rational Field]
列出给定前导子的所有曲线数：
c = CremonaDatabase()
c.number_of_curves(9920)
70
FSD猜想。千年问题：
c = CremonaDatabase()
c.allbsd(11)
{';a1';: [';5';, ';1.2692093042795534217';, ';0.25384186085591068434';, ';1';,
';1.00000000000000000000';], ';a3';: [';1';, ';6.3460465213977671084';,
';0.25384186085591068434';, ';1';, ';1';], ';a2';: [';1';,
';0.25384186085591068434';, ';0.25384186085591068434';, ';1';,
';1.00000000000000000000';]}{';a1';: [';5';, ';1.2692093042795534217';, ';0.25384186085591068434';, ';1';, ';1.00000000000000000000';], ';a3';: [';1';, ';6.3460465213977671084';, ';0.25384186085591068434';, ';1';, ';1';], ';a2';: [';1';, ';0.25384186085591068434';, ';0.25384186085591068434';, ';1';, ';1.00000000000000000000';